What Short Rate Models Represent in Dual-Curve Swaption Calibration

Summary

The document raises a modeling question about interpreting a short rate model calibrated to market swaption volatility in a dual-curve setting. Because a swap may use one curve for floating-rate projections and another for discounting, the author asks what curve the calibrated model represents when used in its pricing formulas: the discount curve, the projection curve, or a combined valuation effect.

It also asks how to simulate curves for swap pricing, including whether one calibrated model can supply both projected rates and discount factors or whether separate models are needed. The document provides no answer, calibration framework, or empirical evidence, so it serves as a statement of the modeling problem rather than a solution. In practice, resolving it requires specifying the model's rate representation, the curves and instruments used for calibration, and how dependencies between projection and discount rates are modeled.

Key ideas

• Dual-curve swap pricing separates floating-rate projection from discounting.
• Swaption volatility calibration does not by itself explain which curve a short rate model represents.
• Simulated swap pricing requires both projected rates and discount factors.
• The document poses, but does not resolve, whether one model or linked separate models are appropriate.

Tags

# Dual curves and short rate calibration


# Dual curves and short rate calibration












When I calibrate a short rate model to market swaption vols, what curve am I getting when I plug in the calibrated parameters into the analytical formulae (assuming they exist for the model I'm looking at)?

Since swaption vols apply to a swap that is projected and discounted off different curves, I can't get my head around whether the resulting short rate model simulates the discount curve, projection curve or somehow the "total" swap.

I'm basically trying to figure out how to price a swap using simulated curves produced using a short rate model in this new dual curve world. I need projections and discount factors, and I don't know if they should come from one calibrated short rate model, or if I should be somehow have two short rate models (one for the projection curve and one for discount, both maybe calibrated using market swaption vols but different term structures)?

Any help would be appreciated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.